AN EVALUATION OF THE IMPACT OF CARTOGRAPHIC GENERALISATION ON LENGTH MEASUREMENT COMPUTED FROM LINEAR VECTOR DATABASES

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1 CO-086 AN EVALUATION OF THE IMPACT OF CARTOGRAPHIC GENERALISATION ON LENGTH MEASUREMENT COMPUTED FROM LINEAR VECTOR DATABASES GIRRES J.F. Institut Géographique National - Laboratoire COGIT, SAINT-MANDE, FRANCE 1. INTRODUCTION Since three decades, a significant number of researches have been conducted in the field of spatial data quality evaluation (Devillers et al, 2010). Many studies have been published on the estimation of positional accuracy (see, for instance, Burrough, 1986; Guptill and Morrison, 1995; Vauglin, 1997; Hunter and Goodchild, 1997; Shi and Liu, 2000) and indicators for its description are provided in the ISO norm (ISO, 2006). The information on positional accuracy of geographical objects is fundamental to be communicated to the final user, as it evaluates how far a coordinate is from its real location. Another important information concerns the accuracy of length and area measures performed from a given data set. Indeed, many applications in GIS rely on the computation of these measurements, e.g. a travel time by car, or a population density in an administrative entity. Imprecision in length and area computation has been studied by different researchers. For instance, (Chrisman and Yandell, 1988) proposed a statistical model to estimate the error in area computation, (Griffith, 1989) modeled the impact of digitization error on distance and area computation, and (Leung et al, 2004) developed a general framework for error analysis in measurement-based GIS. Besides these important scientific contributions, it is still very complex to communicate imprecision information in length and area computation to the final user, because the geometry of geographical objects can be affected by different processes which impact these computations. The problem is that the knowledge on positional accuracy does not allow to compute the accuracy on length and area measurements because the distribution of errors of position is not homogeneous and greatly depends on the processes used to build the data. To be able to estimate length and area accuracy, all the possible sources of geometric uncertainty need to be modeled. Indeed, different causes in the production and representation processes of vector objects impact measurements. In term of representation processes, we know that measurements can be impacted by: - the projection system used - not taking account of the terrain, involving an under-estimation of lengths and areas For the production processes, measurements are also impacted by: - the digitizing precision of the operator, usually involved by the scale of capture - the precision of the sensor, if the database is produced using a GPS - the polygonal approximation of curves, when objects represented are curved - effects of cartographic generalisation, if the database is captured from maps If a final user wants to assess the measurement imprecision of its database, he has to take into account all these potential sources of error. To fit with this requirement, our research aims at developing a general model which takes into account all the sources exposed above, and to quantify their respective impact, in order to provide information on measurement imprecision. The expression of digitizing error, and polygonal approximation has already been presented in (Girres and Julien, 2010) and the general model in (Girres and Ruas, 2010). In order to complete the expression of production processes impact on measurements, a study of cartographic generalisation effects has to be conducted. In this context, this paper proposes a method to evaluate the effect of cartographic generalisation on length measurement, focusing on road networks. The general methodology, as far as the different steps of the evaluation, is presented afterwards. 2. ASSUMPTION AND GENERAL METHODOLOGY It is well known that cartographic generalisation affects measurements computed on vector objects (Blakemore, 1984; Joao, 1998, Bard, 2004), by modification of their shape and/or position. As shown by (Touya et al, 2010), we know that specific generalisation processes are used according to a specific spatial context. For instance, different automatic generalisation processes have been developed for mountainous (Mustière, 2001), rural (Duchene, 2004) or urban (Ruas, 1999) areas.

2 In this research, we assume that the quantity of length error in a linear vector dataset varies according to the production scale and the spatial context. Thus, the goal of this paper is to propose a method, in order to define a statistical law to assess the length error in linear vector databases, as presented in formula 1. In this function, two unknowns need to be defined: - The spatial context of objects - The scale of representation, which determines the level of generalisation Methods to delineate the spatial context using external datasets are presented in section 3. For roads, three kinds of context are defined because we know that the effects of generalisation are not the same in urban, rural and mountains areas. - In urban area, streets are removed; some thin areas are enlarged. As the consequence, the positional accuracy of roads is a bit degraded (Figure 1a). - In mountains areas or to be more precise in slope areas road bends can overlap (Figure 1b). As a consequence some bends are removed and others are enlarged. We can then make the hypothesis that generalisation has an impact on road length. - In rural area, conflicts are less important, the effect of generalisation is certainly smaller. The determination of the level of generalisation is presented in section 4, using methods based on the symbol thickness. In order to build the statistical law, a study of the distribution of length errors is realised, based on comparisons between generalised datasets (at different scale levels) with a more accurate and nearly not generalised one, considered as a reference. The methodology of comparisons, performed in the three spatial contexts evocated above, is exposed in the section 5. The process of length imprecision estimation is then divided in two steps: - The elaboration of the function using length comparisons between generalised datasets and a reference dataset, at different scale levels and spatial contexts (Figure 2a) - The use of this function in order to evaluate length imprecision in a dataset, by determining its scale level and spatial contexts (Figure 2b) Experimentation is performed using different representations of a road network in the French department of Pyrénées-Atlantiques. 3. SPATIAL CONTEXT DETECTION

3 As exposed previously, we assume that the effects of cartographic generalisation vary according to the spatial context. Thus, to allow the estimation of length measurement imprecision, the delineation of mountainous, urban, and rural areas needs previously to be done. Because the model is supposed to work for any user, without acquisition of paying data, all the external datasets used in this part are freely downloadable on the Internet Mountainous areas As denominated by «mountainous areas», we actually look for detecting areas with important differences in altitude, because they strongly impact roads (by bend overlaps ) involving generalisation processes. Several methods for the automatic delimitation of mountainous areas have already been developed, as the one proposed by (Chaudhry and Mackaness, 2008a). For this study, an original method is used, based on contour lines. Mountainous area delimitation is realised using contour objects extracted from the SRTM (file srtm_36_04.tif), a 90*90 meters ground resolution digital elevation model, downloaded from Contour lines are created with an equidistance of 40 meters, for the French department of Pyrénées-Atlantiques (Figure 3), using Quantum GIS software ( A grid approach is developed to delineate mountainous areas. A 500*500 meters cell size grid is created on the entire study area. In each cell of the grid, two different criteria are tested in order to determine if the cell is considered as mountainous or not. The first criterion consists in determining the maximum altitude difference between contour lines intersected by the cell, as exposed in formula 2. The second criterion, proposed by (Jaara and Lecordix, in press), takes more into account the altitude heterogeneity in each cell, as shown in Formula 3. After different tests of the two criteria and validation by comparing with maps, the second criterion appeared obviously as the most realistic, using a threshold of 200 meters for a 500*500 meters resolution cell size (Figure 4a). In order to provide a clean and homogeneous delineation of mountainous areas (Figure 4b), two post processing are performed: - Suppression of small polygons (area < sq. meters) - Suppression of holes in polygons

4 The delimitation of mountainous areas was successful in the study zone using a threshold of 200 meters for a resolution cell size of 500*500 meters. Nevertheless, in order to validate the method, it looks important to perform similar experimentations in others areas, using different cell sizes Urban areas Urban area delimitation has been widely studied in the field of cartographic generalisation. Different methods of identification of urban boundaries have been already developed, based on the proximity of buildings (Boffet, 2000; Chaudhry and Mackaness, 2008b), or using road networks density (Walter, 2008). Because buildings or road networks datasets are not systematically available and/or complete on a given area, we decide to use the freely downloadable Corine Land Cover vector database (see Figure 5a). This database, initiated by the European Environment Agency, proposes a land cover classification for European countries in 44 classes. Two of them are provided to delineate urban areas: Continuous Urban Areas and Discontinuous Urban Areas (respectively identified by the codes 111 and 112). A simple Union of these two layers is performed to provide the delimitation of urban area for the study (Figure 5b) Because the Corine Land Cover database is only provided for European Union, the question of the possibilities to delineate urban areas for the other continents needs to be asked. The Global Land Cover Facility (GLCF) also provides land cover classifications and integrates a class Urban and Built at a minimal resolution of 1 square kilometer. Otherwise, methods evocated above, based on buildings and road networks - if available - can be performed Rural Areas In this study, rural areas are defined as the complementary part of the union between mountainous and urban areas, as exposed in Formula 4. After delimitation of the three spatial contexts, a method to estimate the scale of representation of the dataset is proposed, in order to evaluate its level of generalisation. 4. ESTIMATION OF THE LEVEL OF GENERALISATION After presenting methods to detect the spatial context of objects, we describe in this section how to evaluate the level of cartographic generalisation in a dataset. The level of generalisation of a map mainly depends on the scale, the size of the symbol and the spatial context. Moreover, according to a given problem of representation (symbols overlap for instance), specific operations are performed (displacement, bends removal, bends enlargement ). In this way, knowledge on cartographic generalisation operations can help us to estimate the scale of representation, when the symbol size is specified. Thus, two original methods are presented in this section to try to estimate the scale of representation of geographic objects, using samples of road networks Road symbols overlap The first method is related to a classical problem in cartographic generalisation: the representation of close roads. As illustrated in Figure 6, considering that the symbol size is constant, when two roads are close enough, if the scale is reduced, both symbols will overlap, involving an operation of displacement of roads axis for a good representation of the symbols on the map.

5 We assume that the minimal distance computed between two roads axis in a generalised dataset is function of the symbol size and the scale of representation, as exposed in Formula 5. According to map usages, a gap can be provided between two road symbols, to facilitate visualization. Using Formula 5, we can estimate the scale of representation of the map when: - the minimum deviation between close roads is computed (i.e. MRD) - the symbol size is specified (i.e. SSW) To automatically operate this estimation of the scale of representation on a road network dataset, a process has been developed with the Geoxygene Library (Bucher et al, 2009). This estimation supposes the knowledge of the symbol size. We used specifications of roads representation in two maps produced by the IGN, the French National Mapping Agency, presented in Table 1. An algorithm is developed based on the symbol size and the possible scale of representation. In order to locate close roads, potentially affected by symbols overlap, a topological network is created with the road network (Figure 7a). In a second time, intersections of roads (considered as nodes with three or more connected arcs) are selected (Figure 7b). Close intersections, with a distance smaller than 400 meters, are then selected (Figure 7c). All arcs connected to these intersections are finally selected (Figure 7d). For these arcs, we compute a buffer using the product between the selected symbol size and the scale of representation (Figure 7e). If there is no overlap between buffers, the scale is incremented and the process starts again. The algorithm stops when symbols overlap occur between two buffers (Figure 7f), determining an estimation of the scale of representation. In order to validate the proposed method, experimentations have been performed on two databases samples, representing the same road network at two different scales: 1: (TOP100 dataset) and 1: (Regional Map dataset). The initial tested scaled is 1:10 000, incremented by For each scale, the number of overlaps is computed.

6 As exposed in the Figure 8, this method proposes relevant results for the TOP100 dataset. Even if two overlaps are detected at the scale 1:60000, the number significantly increases at the scale 1:100000, the representation scale of the source map. This evaluation is not so obvious on the Regional Map dataset, even if a small peak is observed at the scale 1: Thus, this method provides interesting information to estimate the scale of representation of a generalised dataset. However, this method is effective when the road network is relatively dense, but in mountainous or rural areas, if roads are not close enough, this method becomes useless. Then, a second method is proposed, based on road bends symbols coalescence Road bends symbol coalescence The problem of bends symbol coalescence is also a classical problem in cartographic generalisation. As illustrated in Figure 9 by (Mustière, 2001), when bends are too narrow, a symbol coalescence occurs, avoiding a good visualization of the road sinuosity on the map. Two generalisation processes are proposed in order to provide a good visualization: bends removal or bends enlargement. In order to detect when it is necessary to activate these generalisation processes, (Mustière, 2001) proposed a method based on the maximum tolerated symbol coalescence in road bends. As evocated in Figure 10, when the distance D between the interior of the bend and the symbol boundary is longer than the distance presented in formula 6, the road symbol is considered coalescent and generalisation process needs to be activated.

7 Thus, in order to estimate the scale of representation of generalised objects, we assume that in a road dataset, the maximum tolerated distance between the axis of the road and the symbol boundary complies with Formula 6. To implement this method, an algorithm is developed based on the symbol size and the scale of representation. As in the symbols overlap method presented above, a buffer is build for each road segment, according to map specifications. For each scale experimented, the algorithm compute the number of bends coalescence (i.e. if the distance between the axis of the road and the boundary of the symbol is longer than the distance D), in order to carry out the scale of the data source. Experimentation is performed using the same road networks than in the previous scale estimation method: 1: (TOP100 dataset), 1: (Regional Map). Also, the initial tested scale is 1:10 000, incremented by As presented in Figure 11, results show that the bends symbol coalescence are already detected at large scales in a small quantity. For the TOP100 dataset, the number of symbol coalescences strongly increases at the scale 1: (i.e. the representation scale of the map), which shows the interest of the method. Results are not as significant for the Regional Map dataset. The number of coalescences detected rises at the scale 1:150000, which is below the real representation scale (i.e. 1:250000). The impact of database generalisation, involving the removal of small roads, can be responsible of the low detection of bends symbol coalescence for the Regional Map. Indeed, most of the interesting bends for this method are located on small sinuous roads. These results, as illustrated by the experimentation on the TOP100 dataset, show that this method can also be relevant to estimate the representation scale of a generalised road network dataset, especially in mountainous areas. Nevertheless, the example of the Regional Map illustrates that the impact of database generalisation, and by consequence the completeness of the dataset, can limit the use of this method for a good scale estimation. 5. ELABORATION OF THE LENGTH IMPRECISION FUNCTION As exposed in the second section of this paper, the objective of this study is to elaborate a function, allowing the estimation of the quantity of length error in a road dataset, caused by effects of cartographic generalisation, according to the spatial context and scale of representation. Methods to detect the spatial context and the scale of representation have already been presented in sections 3 and 4. The last section of this paper consists in the elaboration of the function of length imprecision, using comparisons between generalised road datasets with a more accurate one, considered as reference. Principles of comparisons are previously exposed, followed by results of comparisons and the elaboration of the function Datasets comparison method In order to compare the distribution of length differences between a generalised dataset and a reference, an original method is proposed. Indeed, the easiest method would consist in comparing the lengths of entire corresponding sections in the two datasets, located between two intersections. The main problem is that on a generalised dataset, according to the scale of representation, many of these intersections can be removed. Thus, a method of comparison by sections has been developed for this study (Figure 12).

8 After a preliminary matching of the both road networks, using the algorithm developed by (Mustière and Devogèle, 2008), the reference dataset R is divided in sections of equal length, parameterized by the user. The extremities of these sections (R1, R2 ) are then projected on the generalised dataset (C1, C2 ), in order to divide it in the same number of sections. The length difference between the corresponding sections is then computed and stored in a database, in order to study their distribution with classical indicators (average, median and standard deviation of length differences). Such comparisons are performed in the three spatial contexts evocated in section 3, using different length values for the segmenting of the reference dataset Road networks comparisons results Comparisons are performed using three generalised datasets, all representing the road network of the French department of Pyrennées-Atlantiques: BDCARTO (1:50 000), TOP100 (1: ) and Regional Map (1: ). The BDTOPO dataset is used as a reference to perform comparisons. The Table 2 exposes results of comparisons according to the parameterized segmenting length of the reference dataset. For urban areas, the maximum segmenting length computed is 600 meters. Indeed, in urban areas, few road sections observed are longer than this distance. For mountainous and rural areas, segmenting lengths are performed until 2000 meters. Results show that in mountainous area, length imprecision of road networks is more important than in rural or urban areas, whatever the scale is. The table also shows that there is no significant length difference between road sections located in urban or rural areas. But according to generalisation experts, impacts of cartographic generalisation in urban area are more characterized by operations of displacement of objects, which don t impact significantly their lengths but much more their position. The computation of appropriate distance (i.e. Hausdorff distance and Mean Distance, see Vauglin, 1997) to evaluate positional effects would constitute an interesting complement for this study. Results clearly show that the most important factor of imprecision is the level of generalisation, involved by the scale of representation, followed by the spatial context. As shown in Figure 13a, we can easily observe that between TOP100 and BDCARTO datasets, the average imprecision values are much more

9 important for TOP100 datasets in any spatial context. This figure also shows that the average length difference is not so important between TOP100 and the Regional Map road networks, except in urban areas. The Figure 13b presents a representation of the average relative length error, in percentage of the reference segmenting length. This representation shows that in mountainous areas, length measurements performed on road objects are on average underestimated by about 6% at the scale 1:250000, 5.5% at the scale 1: and 1% at the scale 1: In urban areas, they are on average underestimated by about 5% at the scale 1: and 3% at the scale 1:100000; and in rural areas, by about 4.5% at the scale 1:250000, 3.5% at the scale 1: and 0.5% at the scale 1: This formalization of the average relative length error is relevant in order to elaborate the function of length imprecision estimation for generalised road networks datasets Estimation function As assumed in this paper, the imprecision length of a generalised dataset varies according to the spatial context and the scale of representation of objects in the original map. This study, elaborated with datasets produced for the scales 1:50 000, 1: , and 1: in three different spatial contexts (mountainous, urban and rural areas), allows us to represent the function of average relative length imprecision, as exposed in Figure 14. Even if this representation is an approximation based on a specific experimentation, it provides a good complement of the results proposed by (João, 1998). 6. CONCLUSION AND FURTHER WORKS This paper exposed a general method to estimate the impact of cartographic generalisation on length measurements on a road dataset, for which production processes include generalisation operations. The principal assumption of this research is that the quantity of length error varies according to the scale of representation and the spatial context of geographical objects. Experimentations based on comparisons demonstrate that length imprecision is involved primarily by the scale of representation, and secondarily by the spatial context, especially in mountainous area.

10 Several methods have been developed to delineate the spatial context, to estimate the representation scale of the source map, or also to compare datasets lengths using sections. Further developments are still necessary to validate scale detection methods. On a methodological point of view, the function of estimation of length imprecision has been created using prior comparisons, with different datasets variously affected by database generalisation. Thus, length imprecision results can only be accepted for homologous objects, but neither on an entire dataset. Indeed, not taking into account the completeness of the dataset would represent a methodological failure. For instance, the length imprecision between two points, using two different road networks datasets is not only affected by bends generalisation, but also by network generalisation (which is also a generalisation process) involving the presence or absence of road segments. Further investigations needs to be realised on the impact of completeness in the computation of length for a road network. The methodology has been only applied on road networks. To complete the study of the impact of cartographic generalisation, it looks fundamental to develop similar studies on other themes represented in maps, for both linear and polygonal objects. Thus, this original work, already initiated by (João, 1998), needs to be completed by further investigations, which compose consistent contributions for the development of a general model of estimation of geometric imprecision impact on basic measurements. 7. REFERENCES Bard, 2004, Methode d évaluation de la qualité de données géographiques généralisées. Application aux données urbaines, Thèse de doctorat en informatique, Université Paris VI Boffet, 2000, Creating urban information for cartographic generalisation, 9th International Symposium on Spatial Data Handling (SDH 00), August, Beijing (China) Blakemore, 1984, Generalisation and Error in Spatial Data Bases, Cartographica, Vol. 21 (2), pp Bucher et al, 2009, GeOxygene: built on top of the expertness of the French NMA to host and share advanced GI Science research results, International Opensource Geospatial Research Symposium 2009 (OGRS'09), 8-10 July, Nantes (France) Burrough, 1986, Principles of Geographical information system for Land Ressources assessment, Oxford University Press, 193 pp Chaudhry and Mackaness, 2008a, Creating Mountains out of Mole Hills: Automatic Identification of Hills and Ranges Using Morphometric Analysis, Transactions in GIS, Vol.12 (5), pp Chaudhry and Mackaness, 2008b, Automatic Identification of Urban Settlement Boundaries for Multiple Representation Databases, Computer Environment and Urban Systems, Vol.32 (2), pp Chrisman and Yandell, 1988, Effects of Point Error on Area Calculations : A Statistical Model, Surveying and Mapping, Vol. 48, pp Devillers et al, 2010, 30 years of research on Spatial Data Quality Achievements, failures and opportunities, Transactions in GIS, vol.14 (4), Duchêne, 2004, Généralisation par agents communicants : le modèle CARTACOM. Application aux données topographiques en zone rurale, Thèse de doctorat en informatique, Université Paris VI Girres and Julien, 2010, Estimation of digitizing and polygonal approximation errors in the computation of length in vector databases, Proceedings of the ninth Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, Leicester, UK Girres and Ruas, 2010, Estimation of Imprecision in Length and Area Computation in Vector Databases Including Production Processes Description, 14th International Symposium on Spatial Data Handling (SDH'10), May, Hong Kong Griffith, 1989, Distance calculations and errors in geographic databases, In The Accuracy of Spatial Databases, pp Guptill and Morrison, 1995, Elements of Spatial Data Quality, Elsevier Science, Oxford, U.K Hunter and Goodchild, 1997, A simple positional accuracy measure for linear features, International Journal of Geographical Information Science, Vol.11, (3), pp ISO, 2006, ISO 19138: Geographic information - Data quality measures, International Standardization Organization, 76 pp Jaara and Lecordix, in press, Extraction of cartographic contour lines using digital terrain model (DTM), The Cartographic Journal João, 1998, Causes and Consequences of Map Generalisation, London, Taylor and Francis

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